I know how you feel. There are tons of scary stuff just out of high school. I also have a pretty heavy stutter, took an bachelor in psychology and thought to myself that "I can just work as a researcher, no way I can interact with people on a daily basis". Turns out the older you get the less you care about what other people thing, I now work with the unemployed, have regularly meeting with people that already hate me before they see me, as well as call a lot of random people. Ive had the job for half a year now and only one person has ever reacted negatively. And believe me when I say it I work with some "less gifted" people. No person in medicine is gonna give a shit about your stutter besides yourself. If you get a doctor licence then you are set. After half a year in the field you are gonna stop caring. Dont let this change what you are, what you want. Then you loose.